Minimal Affine Coordinates for SL(3,C) Character Varieties of Free Groups

Details Minimal Affine Coordinates for SL(3,C) Character Varieties of Free Groups Minimal Affine Coordinates for SL(3,C) Character Varieties of Free Groups

2007-09-27

arxiv.org/abs/0709.4403v2

Journal of Algebra, Volume 320, Issue 10, 15 November 2008, Pages 3773-3810

Mathematics

Algebraic Geometry

49 pages, 9 tables; this version (accepted for publication in Journal of Algebra) has some minor corrections, substantial reor

Scientific paper

10.1016/j.jalgebra.2008.06.031

Let X be the moduli of SL(3,C) representations of a rank r free group. In this paper we determine minimal generators of the coordinate ring of X. This at once gives explicit global coordinates for the moduli and determines the dimension of the moduli's minimal affine embedding. Along the way, we utilize results concerning the moduli of r-tuples of matrices in gl(3,C). Consequently, we also state general invariant theoretic correspondences between the coordinate rings of the moduli of r-tuples of elements in gl(n,C), sl(n,C), and SL(n,C).

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